Introduction 1
About This Book 1
Foolish Assumptions 2
Icons Used in This Book 2
Beyond the Book 3
Where to Go from Here 3
Unit 1: Getting Started with Basic Math & Pre-Algebra 5
Chapter 1: Playing the Numbers Game 7
Inventing Numbers 8
Understanding Number Sequences 8
Evening the odds 8
Counting by threes, fours, fives, and so on 9
Getting square with square numbers 9
Composing yourself with composite numbers 10
Stepping out of the box with prime numbers 11
Multiplying quickly with exponents 12
Four Important Sets of Numbers 13
Counting on the counting numbers 13
Introducing integers 13
Staying rational 14
Getting real 14
Chapter 2: The Big Four Operations 15
The Big Four Operations 15
Adding things up: Addition 16
Take it away: Subtraction 16
A sign of the times: Multiplication 17
Doing math lickety-split: Division 18
Applying the Big Four Operations to Larger Numbers 18
Calculating stacked addition 18
Performing stacked subtraction 19
Calculating with stacked multiplication 21
Understanding long division 22
Unit 2: The Big Four Operations: Addition, Subtraction, Multiplication, and Division 25
Chapter 3: Counting on Success: Numbers and Digits 27
Knowing Your Place Value 28
Counting to ten and beyond 28
Telling placeholders from leading zeros 29
Reading long numbers 30
Close Enough for Rock ‘n’ Roll: Rounding and Estimating 30
Rounding numbers 30
Estimating value to make problems easier 32
Practice Questions Answers and Explanations 34
Whaddya Know? Chapter 3 Quiz 35
Answers to Chapter 3 Quiz 36
Chapter 4: Staying Positive with Negative Numbers 37
Understanding Where Negative Numbers Come From 38
Sign-Switching: Understanding Negation and Absolute Value 39
Addition and Subtraction with Negative Numbers 41
Starting with a negative number 41
Adding a negative number 41
Subtracting a negative number 42
Knowing Signs of the Times (and Division) for Negative Numbers 44
Practice Questions Answers and Explanations 47
Whaddya Know? Chapter 4 Quiz 51
Answers to Chapter 4 Quiz 52
Chapter 5: Putting the Big Four Operations to Work 55
Switching Things Up with Inverse Operations and the Commutative Property 56
Getting with the In-Group: Parentheses and the Associative Property 59
Distribution to lighten the load 61
Understanding Inequalities 63
Doesn’t equal (≠) 63
Less than (<) and greater than (>) 63
Less than or equal to (≤) and greater than or equal to (≥) 64
Approximately equals (≈) 64
Moving Beyond the Big Four: Exponents and Square Roots 65
Understanding exponents 66
Discovering your roots 67
Practice Questions Answers and Explanations 69
Whaddya Know? Chapter 5 Quiz 72
Answers to Chapter 5 Quiz 73
Unit 3: Getting a Handle on Whole Numbers 75
Chapter 6: Please Excuse My Dear Aunt Sally: Evaluating Arithmetic Expressions with PEMDAS 77
The Three E’s of Math: Equations, Expressions, and Evaluation 78
Seeking equality for all: Equations 78
Hey, it’s just an expression 78
Evaluating the situation 79
Putting the Three E’s together 79
Introducing Order of Operations (PEMDAS) 80
Expressions with only addition and subtraction 81
Expressions with only multiplication and division 81
Mixed-operator expressions 82
Handling Powers Responsibly 83
Prioritizing parentheses 84
Pulling apart parentheses and powers 85
Figuring out nested parentheses 86
Bringing It All Together: The Order of Operations 87
Practice Questions Answers and Explanations 89
Whaddya Know? Chapter 6 Quiz 98
Answers to Chapter 6 Quiz 99
Chapter 7: Turning Words into Numbers: Basic Math Word Problems 103
Dispelling Two Myths about Word Problems 104
Word problems aren’t always hard 104
Word problems are useful 104
Solving Basic Word Problems 105
Turning word problems into word equations 105
Plugging in numbers for words 109
Send in the clowns 109
Our house in the middle of our street 110
I hear the train a-comin’ 110
Solving More-Complex Word Problems 113
When numbers get serious 113
Too much information 115
Practice Questions Answers and Explanations 120
Whaddya Know? Chapter 7 Quiz 124
Answers to Chapter 7 Quiz 125
Chapter 8: Divisibility and Prime Numbers 127
Knowing the Divisibility Tricks 128
Counting everyone in: Numbers you can divide everything by 128
In the end: Looking at the final digits 128
Count it up: Checking divisibility by adding and subtracting digits 130
Less is more: Checking divisibility by subtracting 134
Cross-checking: Using multiple tests 135
Identifying Prime and Composite Numbers 136
Practice Questions Answers and Explanations 139
Whaddya Know? Chapter 8 Quiz 142
Answers to Chapter 8 Quiz 143
Chapter 9: Divided Attention: Factors and Multiples 145
Knowing Six Ways to Say the Same Thing 146
Understanding Factors and Multiples 146
Finding Fabulous Factors 148
Deciding when one number is a factor of another 148
Understanding factor pairs 148
Generating a Number’s Factors 149
Decomposing a Number into Its Prime Factors 150
Finding the Greatest Common Factor 151
Generating the Multiples of a Number 153
Finding the Least Common Multiple 153
Practice Questions Answers and Explanations 155
Whaddya Know? Chapter 9 Quiz 158
Answers to Chapter 9 Quiz 159
Unit 4: Fractions 161
Chapter 10: Understanding Fractions 163
Slicing a Cake into Fractions 164
Knowing the Fraction Facts of Life 165
Telling the numerator from the denominator 165
Flipping for reciprocals 166
Using ones and zeros 166
Mixing things up 167
Knowing proper from improper 167
Increasing and Reducing Terms of Fractions 169
Increasing the terms of fractions 170
Reducing fractions to lowest terms (simplifying fractions) 171
Converting between Improper Fractions and Mixed Numbers 174
Knowing the parts of a mixed number 174
Converting a mixed number to an improper fraction 175
Converting an improper fraction to a mixed number 176
Comparing Fractions with Cross-Multiplication 178
Working with Ratios and Proportions 180
Practice Questions Answers and Explanations 182
Whaddya Know? Chapter 10 Quiz 188
Answers to Chapter 10 Quiz 189
Chapter 11: Fractions and the Big Four Operations 191
Multiplying and Dividing Fractions 192
Multiplying numerators and denominators straight across 192
Doing a flip to divide fractions 194
Adding and Subtracting Fractions with the Same Denominator 196
Adding and Subtracting Fractions with Different Denominators 198
The easy case: Increasing the terms of one fraction 198
The difficult case: Increasing the terms of both fractions 200
Practice Questions Answers and Explanations 202
Whaddya Know? Chapter 11 Quiz 208
Answers to Chapter 11 Quiz 209
Chapter 12: Mixing Things Up with Mixed Numbers 213
Multiplying and Dividing Mixed Numbers 214
Adding Mixed Numbers 216
Adding mixed numbers that have the same denominator 216
Adding mixed numbers that have different denominators 217
Adding mixed numbers with carrying 217
Subtracting Mixed Numbers 220
Subtracting mixed numbers that have the same denominator 220
Subtracting mixed numbers that have different denominators 221
Subtracting mixed numbers with borrowing 222
Practice Questions Answers and Explanations 225
Whaddya Know? Chapter 12 Quiz 233
Answers to Chapter 12 Quiz 234
Unit 5: Decimals and Percents 241
Chapter 13: Getting to the Point with Decimals 243
Understanding Basic Decimal Stuff 244
Counting dollars and decimals 244
Identifying the place value of decimals 246
Knowing the decimal facts of life 247
Performing the Big Four Operations with Decimals 252
Adding decimals 253
Subtracting decimals 254
Multiplying decimals 256
Dividing decimals 257
Converting between Decimals and Fractions 262
Simple Decimal-Fraction Conversions 262
Changing decimals to fractions 264
Changing fractions to decimals 267
Practice Questions Answers and Explanations 271
Whaddya Know? Chapter 13 Quiz 279
Answers to Chapter 13 Quiz 280
Chapter 14: Playing the Percentages 285
Making Sense of Percentages 285
Dealing with Percentages Greater than 100% 286
Converting to and from Percentages, Decimals, and Fractions 287
Converting Percentages to Decimals 287
Changing Decimals to Percentages 288
Switching from Percentages to Fractions 288
Converting Fractions to Percentages 289
Solving Percentage Problems 290
Figuring out simple percent problems 291
Turning the problem around 292
Deciphering more-difficult percent problems 293
Putting All the Percent Problems Together 294
Identifying the three types of percent problems 294
Solving Percent Problems with Equations 295
Practice Questions Answers and Explanations 299
Whaddya Know? Chapter 14 Quiz 303
Answers to Chapter 14 Quiz 304
Chapter 15: Word Problems with Fractions, Decimals, and Percentages 307
Adding and Subtracting Parts of the Whole in Word Problems 308
Sharing a pizza: Fractions 308
Buying by the pound: Decimals 309
Splitting the vote: Percentages 309
Problems about Multiplying Fractions 310
Renegade grocery shopping: Buying less than they tell you to 310
Easy as pie: Working out what’s left on your plate 311
Multiplying Decimals and Percentages in Word Problems 313
To the end: Figuring out how much money is left 313
Finding out how much you started with 314
Handling Percent Increases and Decreases in Word Problems 316
Raking in the dough: Finding salary increases 316
Earning interest on top of interest 316
Getting a deal: Calculating discounts 317
Practice Questions Answers and Explanations 319
Whaddya Know? Chapter 15 Quiz 322
Answers to Chapter 15 Quiz 324
Unit 6: Reaching the Summit: Advanced Pre-Algebra Topics 327
Chapter 16: Powers and Roots 329
Memorizing Powers and Roots 329
Remembering square numbers and square roots 330
Keeping track of cubic numbers and cube roots 330
Knowing a few powers of 2 and their related roots 331
Changing the Base 332
Negating a number raised to an exponent 332
Finding powers of negative numbers 332
Finding powers of fractions 333
Mixing negative numbers and fractions with exponents 333
Exponents of 0 and Negative Numbers 334
Exponents of 0 334
Negative exponents 335
Fractional Exponents 337
Exponents of 12 337
Exponents of 13 338
Exponents of 14 , 15, 16, and so forth 339
Other fractional exponents 339
Practice Questions Answers and Explanations 341
Whaddya Know? Chapter 16 Quiz 343
Answers to Chapter 16 Quiz 344
Chapter 17: A Perfect Ten: Condensing Numbers with Scientific Notation 347
First Things First: Using Powers of Ten as Exponents 348
Counting zeros and writing exponents 348
Exponential Arithmetic: Multiplying and Dividing Powers of Ten 350
Working with Scientific Notation 352
Writing in scientific notation 352
Understanding order of magnitude 354
Multiplying with scientific notation 355
Dividing with Scientific Notation 356
Practice Questions Answers and Explanations 357
Whaddya Know? Chapter 17 Quiz 360
Answers to Chapter 17 Quiz 361
Chapter 18: How Much Have You Got? Weights and Measures 363
Understanding Units 364
Adding and subtracting units 364
Multiplying and dividing units 364
Examining Differences between the English and Metric Systems 365
Looking at the English system 365
Looking at the metric system 369
Estimating and Converting between the English and Metric Systems 372
Estimating in the metric system 373
Converting units of measurement 375
Converting between English and Metric Units 377
Practice Questions Answers and Explanations 381
Whaddya Know? Chapter 18 Quiz 388
Answers to Chapter 18 Quiz 389
Chapter 19: Getting the Picture with Geometry 393
Getting on the Plane: Points, Lines, Angles, and Shapes 394
Making some points 394
Knowing your lines 394
Figuring the angles 395
Shaping things up 396
Getting in Shape: Polygon (and Non-Polygon) Basics 396
Closed Encounters: Shaping Up Your Understanding of 2-D Shapes 397
Polygons 397
Circles 399
Squaring Off with Quadrilaterals 400
Making a Triple Play with Triangles 403
Getting Around with Circle Measurements 405
Taking a Trip to Another Dimension: Solid Geometry 406
The many faces of polyhedrons 407
3-D shapes with curves 408
Building Solid Measurement Skills 409
Solving Geometry Word Problems 413
Working from words and images 413
Breaking out those sketching skills 415
Practice Questions Answers and Explanations 418
Whaddya Know? Chapter 19 Quiz 425
Answers to Chapter 19 Quiz 427
Chapter 20: Figuring Your Chances: Statistics and Probability 431
Gathering Data Mathematically: Basic Statistics 432
Understanding differences between qualitative and quantitative data 432
Working with qualitative data 433
Working with quantitative data 436
Looking at Likelihoods: Basic Probability 439
Figuring the probability 440
Oh, the possibilities! Counting outcomes with multiple coins 441
Practice Questions Answers and Explanations 444
Whaddya Know? Chapter 20 Quiz 447
Answers to Chapter 20 Quiz 449
Chapter 21: Setting Things Up with Basic Set Theory 451
Understanding Sets 451
Elementary, my dear: Considering what’s inside sets 452
Sets of numbers 454
Performing Operations on Sets 455
Union: Combined elements 455
Intersection: Elements in common 456
Relative complement: Subtraction (sorta) 457
Complement: Feeling left out 457
Practice Questions Answers and Explanations 459
Whaddya Know? Chapter 21 Quiz 461
Answers to Chapter 21 Quiz 462
Unit 7: The X-Files: Introduction to Algebra 463
Chapter 22: Working with Algebraic Expressions 465
Seeing How X Marks the Spot 466
Expressing Yourself with Algebraic Expressions 466
Evaluating Algebraic Expressions 467
Knowing the Terms 470
Making the commute: Rearranging your terms 471
Identifying the coefficient and variable 472
Adding and Subtracting Like Terms 473
Identifying like terms 473
Adding and subtracting terms 474
Multiplying and Dividing Terms 475
Simplifying Expressions by Combining Like Terms 479
Removing Parentheses from an Algebraic Expression 481
Drop everything: Parentheses with a plus sign 481
Sign turnabout: Parentheses with a negative sign 481
Distribution: Parentheses with no sign 482
FOILing: Dealing with Two Sets of Parentheses 484
Practice Questions Answers and Explanations 487
Whaddya Know? Chapter 22 Quiz 495
Answers to Chapter 22 Quiz 496
Chapter 23: Solving Algebraic Equations 499
Understanding Algebraic Equations 500
Using x in equations 500
Choosing among four ways to solve algebraic equations 501
The Balancing Act: Solving for x 503
Striking a balance 504
Using the balance scale to isolate x 504
Rearranging Equations and Isolating x 506
Rearranging terms on one side of an equation 506
Moving terms to the other side of the equals sign 507
Removing parentheses from equations 509
Cross-multiplying 512
Practice Questions Answers and Explanations 515
Whaddya Know? Chapter 23 Quiz 525
Answers to Chapter 23 Quiz 526
Chapter 24: Tackling Algebra Word Problems 531
Solving Algebra Word Problems in Five Steps 531
Declaring a variable 532
Setting up the equation 533
Solving the equation 533
Answering the question 534
Checking your work 534
Choosing Your Variable Wisely 536
Solving More-Complex Algebraic Problems 539
Charting four people 539
Crossing the finish line with five people 540
Practice Questions Answers and Explanations 545
Whaddya Know? Chapter 24 Quiz 549
Answers to Chapter 24 Quiz 550
Chapter 25: Graphing Algebraic Equations 553
Graphing on the xy-Plane 554
Understanding the axes, the origin, and the quadrants 554
Plotting coordinates on the xy-plane 554
Graphing equations on the xy-plane 555
Understanding Linear Equations 559
Knowing the most basic linear equation 559
Changing the slope (m) 560
Changing the y-intercept (b) 561
Understanding slope-intercept form 562
Measuring the Slope of a Line 564
Estimating slope 564
Eyeballing slope on the xy-plane 566
Using the two-point slope formula 569
Graphing Linear Equations Using the Slope and y-intercept 572
Practice Questions Answers and Explanations 574
Whaddya Know? Chapter 25 Quiz 577
Answers to Chapter 25 Quiz 581
Index 583
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